ALBERT

Description: Insight into the global ocean energy cycle and its relationship to climate variability can be gained by examining the temporal variability of eddy–mean flow interactions. A time-dependent version of the Lorenz energy diagram is formulated and applied to energetic ocean regions from a global, eddying state estimate. The total energy in each snapshot is partitioned into three components: energy in the mean flow, energy in eddies, and energy temporal anomaly residual, whose time mean is zero. These three terms represent, respectively, correlations between mean quantities, correlations between eddy quantities, and eddy-mean correlations. Eddy–mean flow interactions involve energy exchange among these three components. The temporal coherence about energy exchange during eddy–mean flow interactions is assessed. In the Kuroshio and Gulf Stream Extension regions, a suppression relation is manifested by a reduction in the baroclinic energy pathway to the eddy kinetic energy (EKE) reservoir following a strengthening of the barotropic energy pathway to EKE; the baroclinic pathway strengthens when the barotropic pathway weakens. In the subtropical gyre and Southern Ocean, a delay in energy transfer between different reservoirs occurs during baroclinic instability. The delay mechanism is identified using a quasigeostrophic, two-layer model; part of the potential energy in large-scale eddies, gained from the mean flow, cascades to smaller scales through eddy stirring before converting to EKE. The delay time is related to this forward cascade and scales linearly with the eddy turnover time. The relation between temporal variations in wind power input and eddy–mean flow interactions is also assessed.

Description: Giant planet tropospheres lack a solid, frictional bottom boundary. The troposphere instead smoothly transitions to a denser fluid interior below. However, Saturn exhibits a hot, symmetric cyclone centered directly on each pole, bearing many similarities to terrestrial hurricanes. Transient cyclonic features are observed at Neptune’s South Pole as well. The wind-induced surface heat exchange mechanism for tropical cyclones on Earth requires energy flux from a surface, so another mechanism must be responsible for the polar accumulation of cyclonic vorticity on giant planets. Here it is argued that the vortical hot tower mechanism, claimed by Montgomery et al. and others to be essential for tropical cyclone formation, is the key ingredient responsible for Saturn’s polar vortices. A 2.5-layer polar shallow-water model, introduced by O’Neill et al., is employed and described in detail. The authors first explore freely evolving behavior and then forced-dissipative behavior. It is demonstrated that local, intense vertical mass fluxes, representing baroclinic moist convective thunderstorms, can become vertically aligned and accumulate cyclonic vorticity at the pole. A scaling is found for the energy density of the model as a function of control parameters. Here it is shown that, for a fixed planetary radius and deformation radius, total energy density is the primary predictor of whether a strong polar vortex forms. Further, multiple very weak jets are formed in simulations that are not conducive to polar cyclones.

Description: In this paper it is proposed that baroclinic instability of even a weak shear may play an important role in the generation and stability of the strong zonal jets observed in the atmospheres of the giant planets. The atmosphere is modeled as a two-layer structure, where the upper layer is a standard quasigeostrophic layer on a β plane and the lower layer is parameterized to represent a deep interior convective columnar structure using a negative β plane as in Ingersoll and Pollard. Linear stability theory predicts that the high wavenumber perturbations will be the dominant unstable modes for a small vertical wind shear like that inferred from observations. Here a nonlinear analytical model is developed that is truncated to one growing mode that exhibits a multiple jet meridional structure, driven by the nonlinear interaction between the eddies. In the weakly supercritical limit, this model agrees with previous weakly nonlinear theory, but it can be explored beyond this limit allowing the multiple jet–induced zonal flow to be stronger than the eddy field. Calculations with a fully nonlinear pseudospectral model produce stable meridional multijet structures when beginning from a random potential vorticity perturbation field. The instability removes energy from the background weak baroclinic shear and generates turbulent eddies that undergo an inverse energy cascade and form multijet zonal winds. The jets are the dominant feature in the instantaneous upper-layer flow, with the eddies being relatively weak. The jets scale with the Rhines length, but are strong enough to violate the barotropic stability criterion. It is shown that the basic physical mechanism for the generation and stability of the jets in the full numerical model is similar to that of the truncated model.

Description: Analysis of spectral kinetic energy fluxes in satellite altimetry data has demonstrated that an inverse cascade of kinetic energy is ubiquitous in the ocean. In geostrophic turbulence models, a fully developed inverse cascade results in barotropic eddies with large horizontal scales. However, midocean eddies contain substantial energy in the baroclinic mode and in compact horizontal scales (scales comparable to the deformation radius Ld). This paper examines the possibility that relatively strong bottom friction prevents the oceanic cascade from becoming fully developed. The importance of the vertical structure of friction is demonstrated by contrasting numerical simulations of two-layer quasigeostrophic turbulence forced by a baroclinically unstable mean flow and damped by bottom Ekman friction with turbulence damped by vertically symmetric Ekman friction (equal decay rates in the two layers). “Cascade inequalities” derived from the energy and enstrophy equations are used to interpret the numerical results. In the symmetric system, the inequality formally requires a cascade to large-scale barotropic flow, independent of the stratification. The inequality is less strict when friction is in the bottom layer only, especially when stratification is surface intensified. Accordingly, model runs with surface-intensified stratification and relatively strong bottom friction retain substantial small-scale baroclinic energy. Altimetric data show that the symmetric inequality is violated in the low- and midlatitude ocean, again suggesting the potential impact of the “bottomness” of friction on eddies. Inequalities developed for multilayer turbulence suggest that high baroclinic modes in the mean shear also enhance small-scale baroclinic eddy energy. The inequalities motivate a new interpretation of barotropization in weakly damped turbulence. In that limit the barotropic mode dominates the spatial average of kinetic energy density because large values of barotropic density are found throughout the model domain, consistent with the barotropic cascade to large horizontal scales, while baroclinic density is spatially localized.

Description: The amplitude, origin, and direction of striations in the subtropical gyre are investigated using simulated and analytical multidimensional spectra. Striations, defined as banded structures in the low-frequency motions, account for a noticeable percentage of zonal velocity variability in the east North Pacific (ENP: 25°–42°N, 150°–130°W) and central North Pacific (CNP: 10°–22°N, 132°E–162°W) regions in an eddying global ocean model. Thus, they likely are nonnegligible in mixing and transport processes. Striations in the ENP region are nonzonal and are embedded in the nonzonal gyre flow, whereas striations in the CNP region are more zonal, as are the mean gyre flows. An idealized 1.5-layer model shows the gyre flow partially determines their directions, which qualitatively resemble those in the global eddying model. In the linear limit, structures are quasi-stationary (frequency ω → 0) linear Rossby waves and the gyre flow influences the direction by influencing the nature of the zero Rossby wave frequency curve. In the nonlinear regime, striations are consistent with the nondispersively propagating eddies, whose low-frequency component has banded structures. The gyre flow influences the striation direction by changing the eddy propagation direction. Their origin in the nonlinear regime is consistent with the existence of a nondispersive line in the frequency–wavenumber spectra. This study does not exclude other striation mechanisms from literature, considering that the interpretations here are based on an idealized model and only from a spectral perspective.

Description: Motivated by the fact that time-dependent currents are ubiquitous in the ocean, this work studies the two-layer Phillips model on the beta plane with baroclinic shear flows that are steady, periodic, or aperiodic in time to understand their nonlinear evolution better. When a linearly unstable basic state is slightly perturbed, the primary wave grows exponentially until nonlinear advection adjusts the growth. Even though for long time scales these nearly two-dimensional motions predominantly cascade energy to large scales, for relatively short times the wave–mean flow and wave–wave interactions cascade energy to smaller horizontal length scales. The authors demonstrate that the manner through which these mechanisms excite the harmonics depends significantly on the characteristics of the basic state. Time-dependent basic states can excite harmonics very rapidly in comparison to steady basic states. Moreover, in all the simulations of aperiodic baroclinic shear flows, the barotropic component of the primary wave continues to grow after the adjustment by the nonlinearities. Furthermore, the authors find that the correction to the zonal mean flow can be much larger when the basic state is aperiodic compared to the periodic or steady limits. Finally, even though time-dependent baroclinic shear on an f plane is linearly stable, the authors show that perturbations can grow algebraically in the linear regime because of the erratic variations in the aperiodic flow. Subsequently, baroclinicity adjusts the growing wave and creates a final state that is more energetic than the nonlinear adjustment of any of the unstable steady baroclinic shears that are considered.

Description: Linear and nonlinear radiating instabilities of an eastern boundary current are studied using a barotropic quasigeostrophic model in an idealized meridional channel. The eastern boundary current is meridionally uniform and produces unstable modes in which long waves are most able to radiate. These long radiating modes are easily suppressed by friction because of their small growth rates. However, the long radiating modes can overcome friction by nonlinear energy input transferred from the more unstable trapped mode and play an important role in the energy budget of the boundary current system. The nonlinearly powered long radiating modes take away part of the perturbation energy from the instability origin to the ocean interior. The radiated instabilities can generate zonal striations in the ocean interior that are comparable to features observed in the ocean. Subharmonic instability is identified to be responsible for the nonlinear resonance between the radiating and trapped modes, but more general nonlinear triad interactions are expected to apply in a highly nonlinear environment.